Question

Find the equation of the line perpendicular to y = - 4x + 8 that passes through the point (8,4).y =

Answer 1

y= (1/4)x+2

Step-by-step explanation:

Comparing y =-4x + 8 to the slope-intercept form y=mx+b

• Slope = -4.

Let the slope of the new line = m

Two lines are perpendicular if the product of their slopes is -1.

Therefore:

`\begin{gathered} -4m=-1 \\ m=(-1)/(-4) \\ m=(1)/(4) \end{gathered}`

The slope of the perpendicular line = 1/4

Since the line passes through the point (8,4), we have:

`\begin{gathered} y-y_1=m(x-x_1) \\ y-4=(1)/(4)(x-8) \\ y=(1)/(4)(x-8)+4 \\ y=(1)/(4)x-2+4 \\ y=(1)/(4)x+2 \end{gathered}`

The equation of the perpendicular line is y= (1/4)x+2